Application of stochastic analysis to ultrasonic echoes—Estimation of attenuation and tissue heterogeneity from peaks of echo envelope

Abstract

A study of the statistics of ultrasound speckle indicates that the noise-to-signal ratio (NSR) of the echo envelope peaks (EEP) in a B scan is monotonically related to the variance of the mean power of the backscattered echoes. If it is assumed that the backscattered echoes all have the same mean power, the NSR of the EEP's in a B scan will be expected to reach a theoretical minimum value NSR0 (0.40 approximately 0.42). In practical situations, the variance of the mean power of the echoes is increased due to the presence of both attenuation (including beam spreading) and the spatial variation in the backscattering cross section (BCS) of the tissue. Accordingly, the measured value of the NSR of the EEP's is expected to be greater than the NSR0. In principle, the effects of beam pattern and the attenuation can be compensated for by system calibration and a depth-related gain function, respectively. The attenuation coefficient of the tissue may then be obtained by adjusting the gain function to minimize the NSR of the EEP's. Due to the random nature of the heterogeneity of diseased tissue, the effect of the variation in the BCS, however, cannot be compensated for by the depth-related gain function. Therefore, the minimum value of the NSR indicates the spatial variation in the BCS and may finally correlate to the disease state of the tissue.